Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Grid point interpolation on finite regions using C1 box splines
SIAM Journal on Numerical Analysis
Computer Aided Geometric Design
Box splines
A new solid subdivision scheme based on box splines
Proceedings of the seventh ACM symposium on Solid modeling and applications
Multidimensional Digital Signal Processing
Multidimensional Digital Signal Processing
Optimal regular volume sampling
Proceedings of the conference on Visualization '01
Spline space and its B-splines on an n + 1 direction mesh in Rn
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
Linear and Cubic Box Splines for the Body Centered Cubic Lattice
VIS '04 Proceedings of the conference on Visualization '04
Discrete Topology of (An*) Optimal Sampling Grids. Interest in Image Processing and Visualization
Journal of Mathematical Imaging and Vision
Journal of Computational and Applied Mathematics
On visual quality of optimal 3D sampling and reconstruction
GI '07 Proceedings of Graphics Interface 2007
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
Optimal sampling lattices and trivariate box splines
Optimal sampling lattices and trivariate box splines
Box Spline Reconstruction On The Face-Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Information Theory
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
Symmetric box-splines on root lattices
Journal of Computational and Applied Mathematics
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Sampling and reconstruction of generic multivariate functions is more efficient on non-Cartesian root lattices, such as the BCC (Body-Centered Cubic) lattice, than on the Cartesian lattice. We introduce a new nxn generator matrix A^* that enables, in n variables, efficient reconstruction on the non-Cartesian root lattice A"n^* by a symmetric box-spline family M"r^*. A"2^* is the hexagonal lattice and A"3^* is the BCC lattice. We point out the similarities and differences of M"r^* with respect to the popular Cartesian-shifted box-spline family M"r, document the main properties of M"r^* and the partition induced by its knot planes and construct, in n variables, the optimal quasi-interpolant of M"2^*.